Short-wave vortex instabilities in stratified flow

vortex;voritices;stability theory;stratified flow;computational fluid dynamics;spectral methods;linear stability theory;fluid dynamics;turbulence;stratified turbulence;Applied Mathematics

Bovard, Luke

University of Waterloo

关键词: vortex;    voritices;    stability theory;    stratified flow;    computational fluid dynamics;    spectral methods;    linear stability theory;    fluid dynamics;    turbulence;    stratified turbulence;    Applied Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/8097/1/Bovard_Luke.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Density stratification is one of the essential underlying physical mechanisms for atmospheric and oceanic flow. As a first step to investigating the mechanisms of stratified turbulence, linear stability plays a critical role in determining under what conditions a flow remains stable or unstable. In the study of transition to stratified turbulence, a common vortex model, known as the Lamb-Chaplygin dipole, is used to investigate the conditions underwhich stratified flow transitions to turbulence. Numerous investigations have determined that a critical length scale, known as the buoyancy length, plays a key role in the breakdown and transition to stratified turbulence. At this buoyancy length scale, an instability unique to stratified flow, the zigzaginstability, emerges. However investigations into sub-buoyancy length scales have remained unexplored. In this thesis we discover and investigate a new instability of the Lamb-Chaplyin dipole that exists at the sub-buoyancy scale. Through numerical linear stability analysis we show that this short-wave instability exhibits growth rates similar to that of the zigzag instability. We conclude with nonlinear studies of this short-wave instability and demonstrate this new instability saturates at a level proportional to the cube ofthe aspect ratio.